What is the required minimum amount of moderately intense physical activity?

Answer 1

150 and 75 per week

Answer 2

With respect to cardio, forget about steady state exercising. Instead, use intense (therefore, brief) exercise such as GXP (Graded Exercise Protocol) or HIIT (High Intensity Interval Training). With respect to resistance training, use perfect exercise technique with the highest resistance possible. Moderate intensity won't stimulate muscular growth.

Alternate Perspective:

If you really want to stick with moderate physical activity, be aware that you are not likely to gain much mass or strength; these qualities arise from pushing your body through its limitations and re-setting the bar. Moderately-intense physical activity is, however, great for building cardiovascular endurance and developing better toning for existing muscle; there are other medical benefits to this as well. Most sources recommend at least 20 minutes per day (minimum) of moderate physical activity, with recommended averages reaching the 60 minute mark. If you engage in high-intensity exercise as suggested in the answer above, that time certainly counts toward the 20-minute minimum.